论文标题
衍生的翻转类别和立方体曲面类别
Derived categories of flips and cubic hypersurfaces
论文作者
论文摘要
邦德 - 奥洛夫（Bondal-Orolov）的经典结果指出，在衍生的连贯滑轮类别之间，偶然几何形状的标准翻转产生了完全忠实的函子。我们通过描述补体来完成它们的嵌入到半三相分解中。作为一种应用，我们可以将“二次狂热对应”（由于galkin shinder引起）（由于galkin shinder），在光滑的立方超表面，其扇形的各种线条和希尔伯特方形之间，将其提升到半双胞线分解之间。 我们还表明，尺寸的立方体超出表面的希尔伯特广场至少3次是一种狂热品种，因此特别是Cubic Hyperface上的Fano种类品种是Fano访问者。最有趣的案例是立方四倍，在该案例中，这表现出了第一个高维超级加尔勒作为Fano访问者的品种。
A classical result of Bondal-Orlov states that a standard flip in birational geometry gives rise to a fully faithful functor between derived categories of coherent sheaves. We complete their embedding into a semiorthogonal decomposition by describing the complement. As an application, we can lift the "quadratic Fano correspondence" (due to Galkin-Shinder) in the Grothendieck ring of varieties between a smooth cubic hypersurface, its Fano variety of lines, and its Hilbert square, to a semiorthogonal decomposition. We also show that the Hilbert square of a cubic hypersurface of dimension at least 3 is again a Fano variety, so in particular the Fano variety of lines on a cubic hypersurface is a Fano visitor. The most interesting case is that of a cubic fourfold, where this exhibits the first higher-dimensional hyperkähler variety as a Fano visitor.
